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I thought the look on his face didn't have anything to do with the riddle's answer. He was about to be told something of vital importance which seemed to be of a secretive nature, which he had previously shown through remarks to his son he thought would be about getting out of there. When the doctor just had a riddle to ask, he was disappointed and probably shocked that that would have been of such a high level of importance to his 'friend' compared to his life. Given where his mind was at the time, I don't think he even tried to solve it, or did so immediately and was even more disillusioned.
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